In a study of the effects of acid rain, a random sample of 100 trees from a particular forest is examined. Forty percent of these show some signs of damage. Which of the following statements is correct? a. None of the aboveb. The sampling distribution of the proportion of damaged trees is approximately Normalc. This is a comparative experiment. d. If a sample of 1000 trees was examined, the variability of the sample proportion would be larger than in a sample of 100 treese. If we took another random sample of trees, we would find that 40% of these would show some signs of damage

Question

Catherine Strong

Mathematics

21 May, 00:33

In a study of the effects of acid rain, a random sample of 100 trees from a particular forest is examined. Forty percent of these show some signs of damage. Which of the following statements is correct? a. None of the aboveb. The sampling distribution of the proportion of damaged trees is approximately Normalc. This is a comparative experiment. d. If a sample of 1000 trees was examined, the variability of the sample proportion would be larger than in a sample of 100 treese. If we took another random sample of trees, we would find that 40% of these would show some signs of damage

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Kc · Answer 1

Answer: b. The sampling distribution of the proportion of damaged trees is approximately Normal

Step-by-step explanation:

The sample mean is an unbiased estimator of the true (unknown) population mean and The sampling distribution shows how the sample mean will vary among repeated samples. In the case above the samples are selected at random from a normally distributed population, and the number of samples selected (n=100) is a bit large therefore the sampling distribution will be approximately normal.